Yes, sometimes header valance will keep door from laying back flat. Use drapery. They make French door rods that mount on wall and swing open with the door.
Always tricky to treat doors! In the past I've used very low profile, cordless pleated shades. They fold up to practically nothing, so during the day are great. (assuming you're only wanting night privacy) Another treatment I've done for a fun statement and privacy are custom roman shades. I've made them myself, and bought them online. They are noticeable during the day, but with beautiful fabric, that's ok. I've got to write a post on just roman shades. That's on my to-do list. Be sure to check back on my DIY & decorating blog for that! Simple Decorating Tips
Here are a few favorite window treatment ideas for French doors. One you can hang curtains out to the sides and draw them as needed. Another is using a frosted film. Here is one I used on French doors. https://amzn.to/2GV2dve